1837 Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces Abstract Ths paper presents an exact model for studyng the global bucklng of conete-flled steel tubular (CFST) columns wth complant nterfaces between the conete core and steel tube. Ths model s then used to evaluate exact tcal bucklng loads and modes of CFST columns. The results prove that nterface complance can consderably reduce the tcal bucklng loads of CFST columns. A good agreement between analytcal and expermental bucklng loads s obtaned f at least one among longtudnal and radal nterfacal stffnesses s hgh. The parametrc study reveals that bucklng loads of CFST columns are very much affected by the nterfacal stffness and boundary condtons. Keywords Bucklng, composte column, steel tubes, conete-flled Smon Schnabl a, * Igor Plannc b a Unversty of Ljubljana, Faculty of Chemstry and Chemcal Technology, Večna pot 113, 1001 Ljubljana, Slovena E-mal address: smon.schnabl@fkkt.un-lj.s b Unversty of Ljubljana, Faculty of Cvl and Geodetc Engneerng, Jamova 2, 1000 Ljubljana, Slovena E-mal address: gor.plannc@fgg.un-lj.s * Correspondng author http://.do.org/10.1590/1679-78253479 Receved 01.11.2016 In revsed form 13.02.2017 Accepted 23.03.2017 Avalable onlne 27.03.2017 NOMENCLATURE A oss-sectonal area (cm 2 ) C radal contact stffness (kn/cm 2 ) D outer dameter of the steel tube (mm) E elastc modulus (kn/cm 2 ) I moment of nerta (cm 4 ) K longtudnal contact stffness (kn/cm 2 ) L column length (cm)
1838 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces NOMENCLATURE (contnuaton) M oss-sectonal bendng moment (kncm) P centrally appled pont force (kn) P tcal bucklng load (kn) p X contact tracton n X drecton (kn/cm 2 ) p Z contact tracton nz drecton (kn/cm 2 ) m contact tracton n drecton (kncm/cm 2 ) R X X component of the oss-sectonal equlbrum force (kn) R Z Z component of the oss-sectonal equlbrum force (kn) t wall thckness of the steel tube (mm) u axal dsplacement (cm) w deflecton (cm) Greek letters d varaton operator D U nterlayer slp (cm) D W nterlayer uplft (cm) e axal stran e tcal axal stran k pseudocurvature (rad/m) l column slenderness rato j rotaton (rad) Superspts layer or materal c conete core s steel tube 1 INTRODUCTION Conete-flled steel tubular (CFST) columns are becomng popular n today's constructon practce. They are used n many structural applcatons ncludng columns supportng platforms of offshore structures and wnd turbnes, roofs of storage tanks, brdge pers, ples, and columns n sesmc zones and hgh-rse buldngs. CFST columns offer major advantages over ether pure steel tubes or conete members. Stffness, strength, ductlty, sesmc and fre resstance, deformaton characterstcs, elmnaton of formwork costs, nstallaton, economy, and good performance are among the advantages acheved n usng such a structural system. Accordngly, a great deal of expermental research works has been done by Zeghche and Chaou (2005), Ellobody et al. (2006), ang and Han (2006), Guo et al. (2007), La and Ho (2014), Feng et al. (2015), and Wang et al. (2015) among many others, to nvestgate the behavour of CFST columns. Alternatvely, much numercal research work has been reported by Shams and Saadeghvazr (1999), Hu et al. (2003), Valpour and Foster (2010), Lang (2011), Tao et al. (2013), Wang and Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1839 oung (2013), Patel et al. (2014), Zhang et al. (2015), Aslan et al. (2015), and analytcal studes by Cho and Xao (2010), Schneder (1998), Brauns (1999), Susantha et al. (2001), Fam et al. (2004), Kuranovas et al. (2009). An up to date revew on steel-conete composte columns ncludng expermental and analytcal studes has been reported by Shanmugam and Lakshm (2001). Lkewse, Han et al. (2014) have revewed the development and advanced applcatons of the famly of CFST structures tll today. CFST columns can sustan large axal loads especally when used n hgh-rse buldngs. Shorter CFST columns may fal by ushng of the conete core or by local bucklng and yeldng of the steel tube, whle on the other hand, slender CFST columns usually fal by overall bucklng. Most of the research on CFST columns covered n the lterature s focused on short CFST columns. However, much less lterature s avalable on global bucklng behavour of slender CFST columns. Thus, only a few papers have dealt wth ths subject, see e.g. Goode et al. (2010), Romero et al. (2011), Portoles et al. (2011), Da et al. (2014), and Hassanen and Kharoob (2014). Note, that to date, only Han (2000) has expermentally nvestgated the bucklng behavor of cular CFST columns wth very hgh slenderness ratos. The above-mentoned research work done on CFST columns s based on a smple predcton of fully bonded connecton between the conete core and the steel tube. Nevertheless, n real stuatons, mperfect nterface complance between the conete core and the steel tube s observed especally when hgh axal loads are consdered. Unfortunately, ths mperfect bondng can reduce the ntal stffness and elastc strength of CFST columns consderably. The stuaton can be even worse n case of hgh-strength CFST columns, see Lao et al. (2011). Despte that, research works on composte acton n CFST columns are stll very lmted n lterature. To date, only a few researchers have studed composte acton n CFST columns; see e.g. Lao et al. (2011), Hajjar et al. (1998), Fam et al. (2004), Roeder et al. (2010). In all of these studes, t has been shown that composte acton n CFST columns s not well understood and thus remans as an nterestng topc for future research. The man purpose of ths paper s the contnuaton work (Schnabl and Plannc, 2015) done on the formulaton of analytcal model for studyng the bucklng behavour of CFST composte columns wth complant nterface between the conete core and steel tube. Thus, the derved mathematcal model s based on the mechancs of layered column theores recently developed by Schnabl et al. (2007), Schnabl and Plannc (2010, 2011a, 2011b, 2013), and Kryžanowsk et al. (2008, 2014). The analytcal model s then used n the numercal examples to show ts applcablty for the analyss of bucklng behavor of CFST columns wth complant nterface and dfferent boundary condtons. 2 PROBLEM FORMULATION 2.1 CFST Column under Consderaton An ntally straght, planar, geometrcally perfect CFST cular column as shown n Fgure 1 s consdered. The CFST column has an undeformed length L and s made from a conete core, c, and a steel tube, s, joned by an nterface of neglgble thckness and fnte stffness n normal and tangental drectons. The CFST cular column s placed n the ( XZ, ) plane of a spatal Cartesan coordnate system wth coordnates ( X,, Z ) and unt base vectors EX, E and EZ = EX E. The Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1840 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces undeformed reference axs of the CFST cular column s common to both layers. It s parameterzed by the undeformed arc-lengthx. Materal partcles of the conete core and the steel tube are dentfed by materal coordnates ( x, y, z ), ( = c, s) n local coordnate system whch s assumed to concde ntally wth spatal coordnates, and then follows the deformaton of the column. Thus, ( x = x = X), ( y = y = ), and ( z = z = Z) n the undeformed confguraton. Further, each materal s modelled by Ressner's large-dsplacement fnte-stran shear-undeformable beam theory (Ressner, 1972). The CFST cular column s subjected to a conservatve compressve load,p, whch acts along the neutral axs of the CFST cular column n such a way that homogeneous stress-stran state of the CFST column n ts prmary confguraton s acheved. For more detals on bucklng behavor of composte columns an nterested reader s referred to the work of Kryžanowsk et al. (2009, 2014), Schnabl and Plannc (2010, 2011a, 2011b, 2013}. Fgure 1: Intal and buckled confguraton of cular CFST column. 2.2 Assumptons In addton to the abovementoned assumptons, a mathematcal formulaton of governng equatons of a cular CFST column s based on the followng assumptons: 1. The materal s lnear elastc. 2. The planar Ressner beam theory (Ressner, 1972) s used for each materal. 3. The shear deformatons are not taken nto account. 4. No local type of nstablty can occur Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1841 5. The materals can slp over each other and separate n radal drecton. 6. The materals are contnuously connected and slp and uplft modul of the connecton are constant. 7. The shapes of the materals oss-sectons are symmetrcal wth respect to the plane of deformaton and reman unchanged n the form and sze durng deformaton. 8. The nterlayer slp and uplft are small. 9. The CFST column s slender. 2.3 Nonlnear Governng Equatons Nonlnear governng equatons of a CFST cular column s composed of knematc, equlbrum, and consttutve equatons along wth natural and essental boundary condtons for each of the materal. Furthermore, there are also constranng equatons whch assemble each ndvdual materal nto a composte structure. A compact notaton ( ) wll be used n further expressons, where = (, c s) ndcates to whch layer the quantty ( ) belongs to. The governng nonlnear equatons of a CFST cular column consttute a system of 12 frst order dfferental equatons wth constant coeffcents for 12 unknown functons u, w, j w, X, Knematc equatons R Z R, M : du 1 + -(1 + e )cosj = 0, (1) dw + (1 + e ) sn j = 0, (2) dj - k = 0, (3) Equlbrum equatons drx px 0, + = (4) drz pz 0, + = (5) dm -(1 + e )( R sn j + R cos j ) + m = 0, (6) X Z Consttutve equatons X Z R cosj - R snj - E A e = 0, (7) M - E I k = 0. (8) Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1842 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces Natural and essental boundary condtons x = 0 S1 + R X (0) = 0 or u (0) = u1, S2 + R Z (0) = 0 or w (0) = u2, S3 + M (0) = 0 or j (0) = u3. (9) x = L X S4 + R ( L) = 0 or u ( L) = u4, Z S5 + R ( L) = 0 or w ( L) = u5, S6 + M ( L) = 0 or j ( L) = u6. (10) uk ands k (k=1,2,,6) mark gven values of generalzed boundary dsplacements and ther comple- mentary generalzed forces at the edges of materals,.e. x = 0 and x = L, respectvely. Constranng equatons and contact model In case of a CFST column a materal s s constraned to follow the deformaton of the materal c, and vce versa, whch means that dsplacements of ntally concdent materal partcles n the contact are constraned to each other. Ths knematc-constrant relaton can be expressed wth the postons of the observed materal partcles n the deformed confguraton X Z R = X E + E + Z E, (11) where the spatal Cartesan coordnates X,, and Z are dependent on the generalzed dsplacements u, w, and j as X = x + u - rsn asn j, (12) = rcos a, (13) Z = w - rsn acos j. (14) A dsplacement vector [[R]] between the two ntally concdent materal partcles that belong to materal c and s, respectvely, s gven as a vector-valued functon by or n component form as éé ùù c s ëë R ûû = R - R = D UEX +DWE Z, (15) c s c s D U ( x, a ) = u -u -r sn a (sn j - sn j ), (16) c s c s D W (, x a ) = w -w -r sn a (cos j - cos j ), (17) Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1843 where respect to the contact, see Fgure 2. DU and DW are the nterlayer slp and uplft between the observed materal partcles wth EX and E Z, and r and a are the polar coordnates of the observed materal partcle n Fgure 2: Cross-secton of a cular CFST column. As a consequence of (15) or (16)-(17), nterlayer contact tractons emerge whose magntudes depend on the type of the connecton. Hence, the contact tractons per unt of the undeformed reference axs of a CFST cular column are expressed as ò 2p p = F( D )d C = F( D ) rd a, (18) X U x U C 0 ò x ò 2p p = G( D )d C = G( D ) rd a, (19) Z W x W C 0 x 2p = ò r DU D W x = - - DU DW C 0 ò ( ) ò ( ) m F( ),0, G( ) d C (0, r cos a, rsn a) F( ),0, G( ) rd a, (20) x where r s the oss-sectonal vector-valued poston functon of the observed materal partcle of the materal n the contact, C x and dc x are the contour and ts dfferental of the oss-secton of layer, see Fgure 2, F and G are expermentally determned (usually by push-out test) non-lnear functons that desbe consttutve contact laws. 2.4 Lnearzed Governng Equatons A lnearzed system of governng equatons for a determnaton of tcal bucklng loads and modes of CFST columns s based on the frst varaton of the nonlnear system (2)-(20) defned here as d d( x, ) = ( x + b), (21) d b b = 0 where s the functonal, x and are the generalzed dsplacement feld and ts nement, respectvely, and b s a small scalar parameter. Therefore, to derve the lnearzed system of governng Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1844 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces equatons for bucklng problem of a CFST column, lnearzed equatons have to be evaluated at the prmary confguraton n whch the CFST column s straght, namely 1 x e =- P, k = 0, u = u (0) -, w = 0, j = 0, D å U = 0, EA å EA EA D W = 0, RX =- å P, EA R Z = 0, M = 0, p X = 0, p Z = 0, m = 0. (22) The lnearzed bucklng equatons are then: d du - de = 0, (23) dw d æ ö 1 + 1 P - dj = 0, EA ç å çè ø (24) d dj - dk = 0, (25) c dr c s d X -2 prk( du - du ) = 0, (26) s dr c s d X + 2 prk( du - du ) = 0, (27) c dr c s d Z -2 prc( dw - dw ) = 0, (28) s dr c s d Z + 2 prc( dw - dw ) = 0, (29) æ ö æ ö c dm c c c EA dw 1 c 3 c s d - P d 1 P drz pr K( dj dj ) 0, - - - - = EA EA çå ç å è ø è ø æ ö æ ö s dm s s s EA dw 1 s 3 c s d - P d 1 P drz pr K( dj dj ) 0, - - + - = EA EA çå ç å è ø è ø (30) (31) dr dm X - E Ade = 0, (32) - E I dk = 0, (33) Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1845 c s c s dd U = du -du -rsn a( dj - dj ), (34) c s, dd W = dw - dw (35) where K and C are the longtudnal and radal contact stffness, respectvely. The system (23)-(35) s a system of 18 lnear algebrac-dfferental equatons of frst order wth constants coeffcents for 18 unknown functons de, dk, d u, w d, dj, d R X, d R Z, ddu, and ddw along wth the correspondng boundary condtons x = 0 S1 + dr X (0) = 0 or d u (0) = u1, S2 + dr Z (0) = 0 or d w (0) = u2, S3 + dm (0) = 0 or dj (0) = u3. (36) x = L S4 + drx ( L) = 0 or d u ( L) = u4, S5 + drz ( L) = 0 or d w ( L) = u5, S6 + dm ( L) = 0 or dj ( L) = u6. (37) uk ands k (k=1,2,,6) mark gven values of generalzed boundary dsplacements and ther complementary generalzed forces at the edges of materals,.e. x = 0 and x = L, respectvely. 2.5 Exact Bucklng Soluton The system (23)-(35) along wth (36)-(37) can be wrtten n compact form as a homogeneous system of 12 frst order lnear dfferental equatons d () x = A () x and (0) = 0, (38) where () x s the egenvector, (0) s the vector of unknown ntegraton constants, and A s the constant real 12 12 matrx. The exact soluton of (38) s gven by; see (Perko, 2001): x = A () x e. (39) The unknown ntegraton constants 0 n (39) are obtaned from (36)-(37). Hence, a system of 12 homogeneous lnear algebrac equatons for 12 unknown ntegraton constants s obtaned as 0 K0 = 0, (40) where K s the tangent stffness matrx. A non-trval soluton of (40) s obtaned from the condton of sngular stffness matrx, e.. Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1846 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces detk = 0, (41) whch forms a lnear egenvalue problem for the tcal bucklng load P and correspondng bucklng modes of the CFST column. 3 NUMERICAL RESULTS AND DISCUSSION 3.1 Comparson wth Expermental Results The exact bucklng loads of slender CFST P-P cular column calculated by the proposed model are compared wth the expermental results obtaned by Han (2000). The geometrc and materal data for sx CFST columns are lsted n Table 1 and shown n Fgure 3. Fgure 3: Geometrc and materal propertes of CFST columns. Exact and expermental tcal bucklng loads for sx CFST columns are summarzed n Table 1 for dfferent K and C, and l. Specmen L l N *, e C P K=10-10 K=10-2 K=10-1 K=1 K=10 K=10 10 SC154-1 415.8 154 342 10-10 177.649 186.475 240.841 293.583 299.955 300.651 10-5 190.091 198.085 246.015 293.684 299.957 300.651 SC154-2 415.8 154 292 10-3 295.729 295.764 296.055 297.769 300.043 300.651 SC141-1 380.7 141 350 10-10 211.918 220.790 279.200 348.563 357.656 358.646 10-5 222.495 230.785 284.381 348.685 357.659 358.646 SC141-2 380.7 141 370 10-3 350.255 350.326 350.909 354.103 357.762 358.646 SC130-1 351.0 130 400 10-10 249.298 258.206 319.942 407.924 420.537 421.908 10-5 258.371 266.861 324.981 408.067 420.538 421.908 SC130-2 351.0 130 390 10-3 408.187 408.322 409.429 415.044 420.664 421.908 * tcal load obtaned expermentally by Han (2000) Table 1: Comparson of exact and expermental tcal bucklng loads of CFST P-P columns for varous K, C, and l, where e = 0, and K and C are n kn/cm 2. From Table 1 t can be seen that a good agreement of the results s obtaned f at least one of nterface stffness (K or C ) s hgh. Otherwse, the exact bucklng loads are sgnfcantly reduced by the nterface complance. For example, the exact bucklng loads are for almost fully debonded layers up to 60 % of those wth completely connected to each other, and n the range of 57-64 % of exper- Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1847 mental results. Furthermore, the exact results for a relatvely stff connecton ( -3 C 10 and K ³1kN/cm 2 ) are wthn 10 % range measured from the mean expermental results. ³ kn/cm 2 3.2 Effect of Interface Complance on Bucklng Loads and Modes A parametrc study s undertaken to nvestgate the effect of nterface complance on tcal bucklng loads and modes of P-P CFST column. For ths purpose, a CFST column wth the same geo- c metrc and materal propertes as specmens SC154-1 and SC154-2 but E = 2840 kn/cm 2 s used n the parametrc analyss, see Fgure 3 and Table 1. The tcal bucklng loads are computed by the proposed exact model for varous nterlayer stffnesses K and C. The results are presented n Table 2 and Fgure 4. P C K 10-10 10-7 10-5 10-4 10-3 10-2 10 5 10-10 179.865835 179.993792 192.105027 255.862874 297.890147 302.479500 302.983390 * 10-5 179.874803 180.002752 192.113187 255.865453 297.890183 302.479501 302.983390 * 10-3 180.759877 180.887039 192.918146 256.119575 297.893746 302.479536 302.983390 * 10-2 188.553682 188.673596 199.977918 258.328044 297.925910 302.479853 302.983390 * 10-1 242.274702 242.329750 247.428743 273.212174 298.226557 302.483009 302.983390 * 1 295.681485 295.682538 295.785453 296.603501 300.001028 302.512517 302.983390 * 10 302.263327 302.263337 302.264356 302.273485 302.353467 302.687190 302.983390 * 10 2 302.911513 302.911513 302.911524 302.911616 302.912526 302.920497 302.983390 * 10 3 302.976203 302.976203 302.976204 302.976205 302.976214 302.976305 302.983390 * 10 5 302.983318 302.983318 302.983318 302.983318 302.983318 302.983318 302.983390 * 10 10 302.983390 * 302.983390 * 302.983390 * 302.983390 * 302.983390 * 302.983390 * 302.983390 * * P * = P, P = P Table 2: Crtcal bucklng loads of cular CFST P-P columns for varous K, C, c wherel = 154, e ¹ 0, E = 2840 kn/cm 2, and C and K are n kn/cm 2. Fgure 4: Densty plot and contours of tcal bucklng load of CFST columns. Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1848 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces Evdently, the effect of the nterface complance on tcal bucklng loads of P-P CFST columns s sgnfcant. It s seen from Table 2 and Fgure 4 that tcal bucklng loads can deease consderably as the nterfacal stffness deeases. However, ths effect s nsgnfcant f at least one among stffnesses s hgh. Note that n the lmtng case when at least one among stffnesses tends to nfnty, the tcal bucklng load becomes K and C ndependent. In ths case, the tcal bucklng load of the CFST column corresponds to a total sum of the tcal bucklng loads of ndvdual materals, namely the bucklng c load of the conete core, P, s and the steel tube, P, respectvely, 2 c c s s * c s p EI + EI = + = 2 P P P ( ), (1 + e) L (42) and s therefore equvalent to P E whch s the Euler bucklng load for the CFST column wth perfectly bonded layers. On the contrary, n the lmtng case when layers are fully debonded, t may be seen that the tcal bucklng load of the CFST column under consderaton s 2 c c c s p EI s s = + = + 2 P P P E A e, (1 + e) L (43) where s P s the axal load carred by the steel tube. Ths result s expected snce the tcal bucklng load of the conete core n ths partcular case s almost as much as 3 tmes lower than the steel tube. At the end of ths example, frst bucklng modes of the ndvdual layers c and s of the CFST P-P composte column are calculated for varous K 'sand C's. The results are plotted n Fgure 5. Fgure 5: Frst bucklng modes of layers c and s, and tcal bucklng loads of CFST P-P composte column for varous values of K s and C s. Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 1849 It can be seen from Fgure 5 that n case of fully debonded materals, when K and C are almost neglgble, only the conete core buckles, whle the steel tube remans straght. However, for all other values of K and C the deformatons of the materals become constraned. Ths effect, however, becomes pronounced for rather rgdly connected materals n ether of the two drectons. Namely, n that case the frst bucklng modes of the two materals practcally concde. 3.3 Effect of Boundary Condtons on Bucklng Loads The effect of dfferent boundary condtons on tcal bucklng loads of cular CFST composte columns s studed usng the exact model developed. The effect s studed for the CFST column (.e., specmen SC154-1) whose geometrc and materal propertes are gven n Fgure 3 and Table 1. The tcal bucklng loads of CFST columns are gven n Table 3 for varous K s and C s and dfferent boundary condtons,.e clamped-free (C-F), clamped-clamped (C-C), and clamped-pnned (C-P). Note, that the same boundary condtons are used for both materals, the conete core and steel tube, respectvely. As would be expected, the nfluence of nterfacal complance s smlarly consderable n all cases of boundary condtons. The tcal bucklng loads deease wth the nease of nterfacal complance. P C 10-10 10-3 K C-F C-C C-P C-F C-C C-P 10-10 44.95092961 719.2112490 367.8313917 75.13464138 1094.182170 590.2955496 10-5 44.95989029 719.2202108 367.8403534 75.13465339 1094.183316 590.2958548 10-3 45.83596664 720.1067487 368.7262276 75.13583959 1094.296689 590.3260369 10-2 52.77689604 728.1035991 376.6569381 75.14637765 1095.317938 590.5973960 10-1 71.11456051 801.7556923 443.5802350 75.23209327 1104.671332 593.0426878 1 75.25042232 1095.460050 588.7376543 75.50198900 1152.866275 604.9510316 10 75.65633017 1199.648599 616.4465577 75.66425898 1201.041703 616.7586267 10 2 75.69672750 1210.070051 619.1620639 75.69773741 1210.082508 619.1655195 10 3 75.70076519 1211.104568 619.4325425 75.70086471 1211.104691 619.4325774 10 5 75.70120931 1211.218272 619.4622827 75.70121211 1211.218272 619.4622827 10 10 75.70121379 1211.219421 619.4625831 75.70121379 1211.219421 619.4625831 Table 3: Crtcal bucklng loads of cular CFST columns for varous K, C, c where l = 154, e = 0, E = 2760 kn/cm 2, and C and K are n kn/cm 2. 4 CONCLUSIONS The paper presented a new mathematcal model for studyng the bucklng behavour of cular CFST slender columns wth complant nterfaces. The model s capable of predctng exact tcal bucklng loads and modes of CFST columns. The effect of nterface complance, and varous other parameters, on tcal bucklng loads of CFST was studed n detal. Based on the results obtaned n the present study, the followng conclusons can be drawn: 1. The exact soluton of the bucklng loads of elastc cular CFST columns wth complant nterface s presented. Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
1850 S. Schnabl and I. Plannc / Bucklng of Slender Conete-Flled Steel Tubes wth Complant Interfaces 2. A good agreement between the exact and expermental bucklng loads of cular CFST composte columns s observed f at least one among longtudnal and radal nterfacal stffnesses s hgh. In the presence of fnte nterfacal complance the tcal bucklng loads are reduced sgnfcantly. 3. The effect of nterface complance on tcal bucklng loads and modes of CFST columns s proved to be sgnfcant. The tcal bucklng loads deease as the nterfacal complance neases. The frst bucklng modes proved to be constraned f a fnte nterfacal complance s present. 4. As would be expected, the parametrc study revealed that the tcal bucklng loads of cular CFST columns are also very much affected by the type of boundary condtons. 5. The results can be used as a benchmark soluton for a bucklng problem of cular CFST columns wth complant nterfaces. References Aslan, F., Uy, B., Tao, Z., Mashr, F., (2015). Behavour and desgn of composte columns ncorporatng compact hgh-strength steel plates. Journal of Constructonal Steel Research 107:94 110. Brauns, J., (1999). Analyss of stress state n conete-flled steel column. Journal of Constructonal Steel Research 49:189 96. Cho, K.K., Xao,., (2010). Analytcal studes of conete-flled cular steel tubes under axal compresson. Journal of Structural Engneerng ASCE 136(5):565 73. Da, D.H., Lam, D., Jamaluddn, N., e, J., (2014). Numercal analyss of slender ellptcal conete flled columns under axal compresson. Thn Walled Structures 77:26 35. Ellobody, E., oung, B., Lam, D., (2006). Behavour of normal and hgh strength conete-flled compact steel tube cular stub columns. Journal of Constructonal Steel Research 62(5):706 15. Fam, A., Qe, F.S., Rzkalla, S., (2004). Conete-flled steel tubes subjected to axal compresson and lateral cyclc loads. Journal of Structural Engneerng ASCE 130(4):631 40. Feng, P., Cheng, S., Ba,., e, L., (2015). Mechancal behavor of conete-flled square steel tube wth FRPconfned conete core subjected to axal compresson. Computers and Structures 123:312 24. Goode, C.D., Kuranovas, A., Kvedaras, A.K., (2010). Bucklng of slender composte conete-flled steel columns. Journal of Cvl and Engneerng Management 16(2):230 6. Guo, L., Zhang, S., Km, W.J., Ranz, G., (2007). Behavor of square hollow steel tubes and steel tubes flled wth conete. Thn Walled Structures 45(12):961 973. Hajjar, J.F., Schller, P.H., Molodan, A., (1998). A dstrbuted plastcty model for conete-flled steel tube beamcolumns wth nterlayer slp. Engneerng Structures 20(8):663 76. Han, L.H., (2000). Tests on conete flled steel tabular columns wth hgh slenderness rato. Advances n Structural Engneerng 3(4):337 44. Han, L.H., L, W., Bjorhovde, R., (2014). Developments and advanced applcatons of conete-flled steel tubular (CFST) structures: Members. Journal of Constructonal Steel Research 100:211 28. Hassanen, M.F., Kharoob, O.F., (2014). Analyss of cular conete-flled double skn tubular slender columns wth external stanless steel tubes. Thn Walled Structures 79:23 37. Hu, H.T., Huang, C.S., Wu, M.H., Wu,.M., (2003). Nonlnear analyss of axally loaded conete-flled tube columns wth confnement effect. Journal of Structural Engneerng ASCE 129(10):1322 9. Latn Amercan Journal of Solds and Structures 14 (2017) 1837-1852
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